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Other Publications Year : 2004

On Tangents to Quadric Surfaces

Abstract

We study the variety of common tangents for up to four quadric surfaces in projective three-space, with particular regard to congurations of four quadrics admitting a continuum of common tangents. We formulate geometrical conditions in the projective space dened by all complex quadric surfaces which express the fact that several quadrics are tangent along a curve to one and the same quadric of rank at least three, and called, for intuitive reasons: a basket. Lines in any ruling of the latter will be common tangents. These considerations are then restricted to spheres in Euclidean threespace, and result in a complete answer to the question over the reals: "When do four spheres allow infinitely many common tangents?".
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Dates and versions

inria-00431701 , version 1 (12-11-2009)

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  • HAL Id : inria-00431701 , version 1

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Ciprian Borcea, Xavier Goaoc, Sylvain Lazard, Sylvain Petitjean. On Tangents to Quadric Surfaces. 2004. ⟨inria-00431701⟩
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